Poisson distribution squared

Question

Let $X$ be a poisson distributed r.v. of parameter $\lambda>0$. Then for any integer $k \geq 0$ is it correct that $$P(X^2=k)=P(X=\sqrt{k})=\lambda^{\sqrt{k}} e^{-\lambda}/\sqrt{k}!$$

where for $\sqrt{k}!$ I mean $\sqrt{k}!= \Gamma (\sqrt{k})$ ?